Weight distributions of the cosets of the (32, 6) Reed-Muller code
E Berlekamp, L Welch - IEEE Transactions on Information …, 1972 - ieeexplore.ieee.org
E Berlekamp, L Welch
IEEE Transactions on Information Theory, 1972•ieeexplore.ieee.orgIn this paper we present the weight distribution of all 2^ 26 cosets of the (32, 6) first-order
Reed-Muller code. The code is invariant under the complete affine group, of order 32 * 31 *
30 * 28 * 24 * 16. In the Appendix we show (by hand computations) that this group partitions
the 2^ 26 cosets into only 48 equivalence classes, and we obtain the number of cosets in
each class. A simple computer program then enumerated the weights of the 32 vectors ih
each of the 48 cosets. These coset enumerations also answer this equivalent problem: how …
Reed-Muller code. The code is invariant under the complete affine group, of order 32 * 31 *
30 * 28 * 24 * 16. In the Appendix we show (by hand computations) that this group partitions
the 2^ 26 cosets into only 48 equivalence classes, and we obtain the number of cosets in
each class. A simple computer program then enumerated the weights of the 32 vectors ih
each of the 48 cosets. These coset enumerations also answer this equivalent problem: how …
In this paper we present the weight distribution of all cosets of the (32,6) first-order Reed-Muller code. The code is invariant under the complete affine group, of order 16. In the Appendix we show (by hand computations) that this group partitions the cosets into only 48 equivalence classes, and we obtain the number of cosets in each class. A simple computer program then enumerated the weights of the 32 vectors ih each of the 48 cosets. These coset enumerations also answer this equivalent problem: how well are the Boolean functions of five variables approximated by the linear functions and their complements?
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